Question

Kelli Blakely is a portfolio manager for the Miranda Fund (Miranda), a core large-cap equity fund. The market proxy and benchmark for performance measurement purposes is the S&P 500. Although the Miranda portfolio generally mirrors the asset class and sector weightings of the S&P, Blakely is allowed a significant amount of leeway in managing the fund. Her portfolio holds only stocks found in the S&P 500 and cash. Blakely was able to produce exceptional returns last year (as outlined in the table below) through her market-timing and security selection skills. At the outset of the year, she became extremely concerned that the combination of a weak economy and geo-political uncertainties would negatively impact the market. Taking a bold step, she changed her market allocation. For the entire year her asset class exposures averaged 50% in stocks and 50% in cash. The S&P’s allocation between stocks and cash during the period was a constant 97% and 3%, respectively. The risk-free rate of return was 2%.

a. What are the Sharpe ratios for the Miranda Fund and the S&P 500?

b. What are the M² measures for Miranda and the S&P 500?

c. What is the Treynor measure for the Miranda Fund and the S&P 500?

d. What is the Jensen measure for the Miranda Fund?

Short answer

a. S_P= .2216 S_M= -.5568

b. 11.75 % and 34.25%

c. S_P= 0.745, S_M= -.245

d.α_P= .3515

Step-by-step solution

Calculation of Sharpe ration of Miranda Fund and S&P 500’a’

S_P= E(r_p – r_f) / P

= .102 - .02 / .37

= .2216

S_M= E(r_M – r_f) / M

= -.225 - .02 / .44

= -.5568

Calculation of M2 measures for Miranda and S&P 500

From the data,

the Miranda Fund’s position should be .44/.37 = 1.1892

the T Bill’s position should be 1 - 1.1892 = -1892 (if borrowing at risk free rate)

Hence the adjusted return r_p= One year trailing return x position + One year trailing return x S&P’s position

= 10.2% x 1.1892 + (-.1892) x (2%)

=.1175

= 11.75 %

Now the difference in adjusted Miranda fund return and the benchmark =

M²= r_P – r_M

= 11.75 – (-22.50)

=34.25%

Calculation of Treynor measure

T_Miranda= r_P – r_f /β_P

= .102 - .02 / 1.10

= 0.745

T_S&P= r_P – r_f /β_P

= -.225 - .02 / 1.00

= -.245

Calculation of Jensen measure

α_P= E(r_P) -[r_f +β_P[E₍r_{M) -}r_f]

= .102 -[.02 + 1.10 x (-.225 -.02)

=.3515